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We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images, power spectra, point clouds of particles, and so on. The regression seeks a curve in the Wasserstein space that passes closest to the dataset. Our regression problem allows utilizing general curves in a Euclidean setting (linear, quadratic, sinusoidal, and so on), lifted to corresponding measure-valued curves in the Wasserstein space. It can be cast as a multi-marginal optimal transport problem that allows efficient computation. Illustrative academic examples are presented.
We study multi-marginal optimal transport, a generalization of optimal transport that allows us to define discrepancies between multiple measures. It provides a framework to solve multi-task learning problems and to perform barycentric averaging. How
Reducing global carbon emissions will require diverse industrial sectors to use energy more efficiently, electrify, and operate intermittently. The water sector is a transformation target, but we lack energy quantification tools to guide operational,
Recent years have seen an increased interest in using mean-field density based modelling and control strategy for deploying robotic swarms. In this paper, we study how to dynamically deploy the robots subject to their physical constraints to efficien
Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational requirements. This
This paper investigates an optimal consensus problem for a group of uncertain linear multi-agent systems. All agents are allowed to possess parametric uncertainties that range over an arbitrarily large compact set. The goal is to collectively minimiz